ON THE ACTION OF MAGNETISM ON LIGHT. 339 



the motion for the case when u> is very great compared with n loses its 

 original character, and reduces to a form which, neglecting slight tremors, 

 is derived approximately from the superposition of two circular motions, 

 one in the same direction as the angular velocity w, of period 27r/(7, the 

 other in the opposite direction, of period 2ir/p, where 



1 X-t IX* , 1 \4 1 \4 



'^ 8 w'n 8 w** 8 wm 8 w^ 



The rotation in such a case as this becomes dominant ; a plane oscil- 

 lation now subsists, but will rotate steadily round the axis with angular 

 velocity ^(" — p), which is the slower the greater the velocity w with 

 which the horizontal arm is carried round. 



These results may be extended to any rotating system with two 

 transverse principal periods. Thus for the case of a long stretched cord, 

 or a long rod, rotating round its own length with an angular velocity w 

 which is very great compared with either of its natural transverse fre- 

 quencies (2tt/1)~^ and {2Tr/m)~-, the period of vibration of a wave of 

 given type on the rotating cord will be changed to 



27r / 1 X" \-i 



71 y-'^8u,v) ' 



and the angle of rotation of its plane of polarisation, during propagation 

 through a wave-length, will be 



ttX* 



this rotation being in the same direction as the angular velocity u>. 



Again, this aeolotropic cord may have imposed on it such a (slight) 

 rate of twist that a very long plane wave, made helicoidal by the rota- 

 tion w, will just be straightened out again by this twist, as it progresses 

 along the cord, the natural period being still practically unaltered. From 

 this remark it follows that 'the effect of a twist amounting to one turn 

 in a length s, a small fraction of the wave-length, is to cause the plane 

 of vibration of a wave to turn round with the forward propagation of 



n* 

 the wave, at the rate of one turn in 8 r— 3 wave-lengths,' in the same 



direction as the imposed twist. 



The first of these results illustrates magnetic rotation, the second the 

 axial rotation of quartz ; while a medium filled with spiral arrangements, 

 like the second but devoid of special orientation, represents the rotation 

 of turpentine. The mode of passing directly in this illustration from 

 the efiect of spin to the effect of helical structure produced by twist 

 is noteworthy. 



The subject of a vibrating chain loaded with gyrostats, having their 

 axes all along it, is considered by Lord Kelvin in a later paper : ' and the 

 general behaviour, as to propagation of waves, of a chain loaded with 

 gyrostats which are orientated in any orderly manner with respect to it, 

 has also been developed.^ 



' W. Thomson, Proc. Land. Math. Soc, vi. 1875. 

 ' J. Lartnor, Proc. Lond. Math. Soc, xxi. 1890. 



z 2 



